In the process of MEMS manufacturing, microstructures are usually encapsulated in a sealed micro cavity to maintain vacuum conditions for a proper operation of the MEMS device. Micro cavities have a very small volume (typically 200×200×2 μm3) and the vacuum will be easily spoiled by a leak or out-gassing. It is therefore important to have a means to monitor the pressure in the micro cavity either during product release, during qualification of the production process, or even during operation of the resonant MEMS device.
FIG. 1 shows the pressure dependency of the oscillation amplitude (S12) for a bulk mode timing resonator with a frequency of 25.8 MHz. For pressures above 10 mbar (1 kPa) resonance amplitude starts to deteriorate.
High frequency (HF) resonators (up to 100 MHz but typically lower for bending mode resonators than for bulk mode resonators) suitable as timing devices for MEMS oscillators have limited Q factor due to air damping when the pressure range is above 1 mbar, as can be seen in FIG. 1. A resonator functioning as a timing device should give constant performance (stable frequency and sufficient amplitude for the oscillation), so that operation in a vacuum is desired. A pressure sensor to test the cavity vacuum of MEMS resonators in batch production should therefore be more sensitive to the lower pressures than the HF timing device itself. It should further be integrated in the MEMS micro cavity if possible.
Several concepts of pressure sensors are known, for instance:
Pirani heat wire, based on heat conductivity of gas;
Diaphragm, based on membrane deflection;
Hot and cold cathode, based on ionization of gas. For high-aspect ratio miniaturization like in MEMS devices, however, extremely high magnetic fields will be necessary to reach sufficiently long electron paths and thus sensitivity to the pressure of the gas;
Resonant cantilevers and tuning forks of quartz and silicon, based on damping forces of the gas.
The pressure dependence of the performance of resonant MEMS devices, like resonators and gyroscopes, is the result of damping effects. The equation of motion is:m*a+b*v+k*x=F  (1)
in which:
m is the effective resonator mass;
a is the acceleration;
b is the damping coefficient;
v is the velocity;
k is the spring constant;
x is the displacement; and
F the driving force such as the electrostatic force over the electrode gap.For a solution x=A sin(ω*t),  (2)
The potential energy term of the spring has a magnitude proportional tom*A*ω2  (3)
and the same holds for the kinetic energy of the force after substitution ofω2=k/m.  (4)
While the damping term has a magnitude ofb*A*ω.  (5)
If damping term (5) is comparable to kinetic energy term (3) then damping is considerable. For higher frequency devices damping is comparatively lower. Based on this principle, pressure sensors have been derived that measure changes in amplitude or dissipation. However, the motional resistance of mechanical resonators is not very stable over time, which makes these sensors unreliable in measuring absolute pressure over time, particularly low pressures.
There is therefore a need for pressure sensor approach which is more stable and can be easily implemented using the same technology as the MEMS device for which the pressure sensing is desired.